Question

A contestant on a game show is asked two questions. The probability that she gets the first question correct is 0.3 and the probability that she gets the second question correct is 0.4 . Given that the probability that she gets both questions correct is 0.1 , calculate the probability that: (i) she gets either the first, the second or both questions right (ii) she gets both questions wrong.

Answer 1

The probability of the contestant getting either the first, the second, or both questions right is 0.6. The probability of the contestant getting both questions wrong is 0.4.

Step-by-step explanation:

To calculate the probability that the contestant gets either the first, the second, or both questions right, we can add the probabilities of each event happening individually and subtract the probability of both events happening:

P(Either question 1 or question 2 or both) = P(Q1) + P(Q2) - P(Q1 and Q2)

Using the given probabilities:

P(Either question 1 or question 2 or both) = 0.3 + 0.4 - 0.1 = 0.6

To calculate the probability that she gets both questions wrong, we can subtract the probability of getting at least one question right from 1:

P(Both questions wrong) = 1 - P(Either question 1 or question 2 or both)

P(Both questions wrong) = 1 - 0.6 = 0.4