Please answer ALL questions. Thank you. 1. Given that the probability that an ar

Question

Please answer ALL questions. Thank you.

1. Given that the probability that an archer hits the target with each arrow he shoots is 0.85 (a) Suppose that a random variable Yis defined to take the value 1 when the archer hits the target and 0 when she misses. What is the mean of the random variable (b) The archer shoots 6 arrows. What is the expected number of arrows that hit the target? (c) The archer shoots arrows repeatedly until he hits the first target. What is the expected value number of arrows he shoots? 2. The probability that a student passes Biology is 0.35 and the probability to pass Chemistry is 0.63. If the probability to pass both Biology and Chemistry is 0.4, what is the probability that he will pass either Biology or Chemistry? 3. The ticket machine in a car park takes 50 cent coins and $1 coins. A ticket costs $1.50 The probability that the machine will accept a particular 50 cent coin is 0.9 and that it will accept a particular $1 coin is 0.8 Mary puts one 50 cent coin and one $1 coin into the machine What is the probability that the machine will not accept either of these coins? 4. A computer chip is manufactured by 3 different suppliers. It is known that 5% of chips from Supplier A, 3% from Supplier B, and 8% from Supplier C are defective. If one chip is selected from each supplier, compute the probability that at least one of the chips is defective

Explanation / Answer

2 ) Given that

P(B) = 0.35
P(c) = 0.63
P(B and C) = 0.4

Now we know that

P(B) + P(C) - P(B and C) = P(B or C)

so we calculate the value as
0.35 + 0.63 -0.4 = 0.58

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