[SOLVED] 2 Easy questions I guess...how do I do these problems?

#1 $Old$ March 19th, 2007, 05:52 PM

#1) Suppose that there are 10 candidates for a prospective job, and only 3 of them have taken STA 2023 in the past. If you select two candidates at random from these 10, what is the probability that both candidates have taken STA 2023 in the past? Please type your answer in as a percentage, rounded to the nearest whole percent. (NOTE: Do NOT round any decimals or percentages in the middle of your calculations. Only round your final answer.)

#2) Suppose you are playing a game that involves a spinner with 4 possible results. The spinner lands in the red zone 20% of the time, the yellow zone 30% of the time, the green zone 35% of the time, and the purple zone 15% of the time. Assume each spin is independent of all other spins. In the game, you spin twice in a row on a single turn. Let A = {1st spin of a turn lands in the red zone} and B = {2nd spin of a turn lands in the yellow zone}. In a single turn, what is P(A or B)?

Soroban · #2 $Old$ March 20th, 2007, 01:34 PM

Hello, YogiBear21!

Quote:

1) Suppose that there are 10 candidates for a prospective job,
and only 3 of them have taken STA 2023 in the past.
If you select two candidates at random from these 10, what is the probability
that both candidates have taken STA 2023 in the past?

P(1st took STA2023) .= .3/10
P(2nd took STA2023) .= .2/9

P(both took STA2023) .= .(3/10)·(2/9) .= .1/15 .≈ .7%

Quote:

#2) Suppose you are playing a game that involves a spinner with 4 possible results.
The spinner lands in the red zone 20% of the time, the yellow zone 30% of the time,
the green zone 35% of the time, and the purple zone 15% of the time.
Assume each spin is independent of all other spins.

In the game, you spin twice in a row on a single turn.
Let A = {1st spin of a turn lands in the red zone}
and B = {2nd spin of a turn lands in the yellow zone}.

In a single turn, what is P(A or B)?

We are given: .P(A) = 0.2, .P(B) = 0.3

. . Since the events are independent: .P(A ∩ B) = (0.2)(0.3) = 0.06

Formula: .P(A U B) .= .P(A) + P(B) - P(A ∩ B)

. . Therefore: .P(A U B) .= .0.2 + 0.3 - 0.06 .= .0.44