Given the following probabilities, which event is most likely to occur?
P(A) = 0.2 B. P(B) = 1/6 C. P(C) = 0.3 D. P(D)= 1/3
Answer: D. P(D)=1/3
Working: the possibility is 33.3%, which is the highest of the options
Three events, A, B, and C, are all equally likely. If there are no other possible events, which of the following statements is true?
P(A) = 0 B. P(B) = 1/3 C. P(C) = 1 D. P(A) = 3
Answer: B. P(B) =1/3
Working: Only one of the three possibilities can be the outcome .
The odds in favour of Macy passing her driver’s test, on the first try are 7:4. Determine the odds against Macy passing her driver’s test on the first try.
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4:7 B. 4:11 C. 7:11 D. 3:11
Answer: A. 4:7
Working: 4:7 is the odds against Macy passing the test on the first try.
A credit card randomly generates temporary three-digit pass codes for cardholders. The passcode will consist of three different even digits. Determine the total number of pass codes using three different even digits.
5 P 5 B. 5 P 3 C. 5 P 4 D. 5 P 1
Answer: B. 5 P 3
Nine boys and twelve girls have signed up for a trip. Only six will be selected to go on the trip. Determine the probability that only boys will be on the trip.
0.02% B. 0.08% C. 0.15% D. 0.23%
Answer: C 0.15%
Working: ( 21 C 6 )
Hillary draws a card from a well-shuffled standard deck of 52 playing cards. Then she draws another card from the deck without replacing the first card. Determine the probability that both cards are hearts.
1/20 B. 1/17 C. 1/12 D. 1/8
Answer: B. 1/17
Working: (13/52 x 12/51 = 1/17)
Min draws a card from a well-shuffled standard deck of 52 playing cards. Then she puts the card back in the deck, shuffles again, and draws another card from the deck. Determine the probability that both cards are face cards.
1/125 B. 9/169 C. 7/99 D. 4/25
Answer: B. 9/169
Working: (12/52 x 12/52 = 9/169)
Select the events that are dependent.
A. Drawing a face card from a standard deck of 52 playing cards, putting it back, and then drawing another face card
B. Rolling a 4 and rolling a 3 with a pair of six-sided dice, numbered 1to 6.
C. Drawing a heart from a standard deck of 52 playing cards, putting it back, and then drawing another heart.
D. Rolling a 3 and having a sum greater than 5 with a pair of six-sided dice, numbered 1 to 6
Answer: D. Rolling a 3 and having a sum greater than 5 with a pair of six-sided dice, numbered 1 to 6
Select the events that are independent
A. Drawing a 10 from a standard deck of 52 playing cards and then drawing another card without replacing the first card
B. Rolling a 4 and rolling a 5 with a pair of six-sided dice, numbered 1 to 6
C. Choosing a number between 1 and 20 with the number being a multiple of 3 and also a multiple of 9
D. Drawing a diamond without replacing the first card
Answer: B. Rolling a 4 and rolling a 5 with a pair of six-sided dice, numbered 1 to 6
There are 60 males and 90 females in a graduating class. Of these students, 30 males and 50 females plan to attend a certain university next year. Determine the probability that a randomly selected student plans to attend the university.
0.41 B. 0.47 C. 0.53 D. 0.59
Answer: C. 0.53
Working: (P(Uni) = 30+50/150 = 80/150 = 0.53)
A three-colour spinner is spun, and a die is rolled. Determine the probability of spinning blue and rolling a 4.
1.24% B. 5.56% C. 7.17% D. 9.82%
Answer: B. 5.56%
Working: (1/3 x 1/6 = 1/18 = 0.0555 = 5.56%)
Two cards are drawn, without being replaced, from a standard deck of 52 playing cards. Determine the probability of drawing a face card then drawing an even numbered card.
1.96% B. 9.05% C. 14.32% D. 23.08%
Answer: B. 9.05%
Working: (12/52 x 20/51 = 0.09049 = 9.05%)
Select the independent events.
A. P(A) = 0.22, P(B) = 0.39, and P(A x B) = 0.072
B. P(A) = 0.18, P(B) = 0.7, and P(A x B) = 0.163
C. P(A) = 0.51, P(B) = 0.1, and P(A x B) = 0.069
D. P(A) = 0.9, P(B) = 0.23, and P(A x B) = 0.207
Answer: D. P(A) = 0.9, P(B) = 0.23, and P(A x B) = 0.207
Working: (Events are independent if P(A) x P(B) = P(A.B) and that is the case for only option D)
There are three children in the Jaffina family. Determine the probability that they have two boys and a girl.
12.5% B. 25% C. 37.5% D. 50%
Answer: C. 37.5%
Working: (From a probability tree diagram we get 3/8 x 100 = 37.5%)
