Question

I am wondering if you can help me out with these questions. I am very confused.

1. A math teacher gave her class two tests. While 70% of the class passed the first test and 75% of the class passed the second test, only 65% of the class passed both. Given that the students failed the first test, what probability of those will passed the second test?

2. In the game of roulette, a player can place a $5 bet on the number 8 and have a 1/40 probability of winning. If the metal ball lands on 8​, the player gets to keep the ​$5 paid to play the game and the player is awarded an additional ​$220. Otherwise, the player is awarded nothing and the casino takes the player’s $5. If you played the game 10 times, what is the variance of your winnings? If you played the game 100 times, what is the standard deviation?

Answer 1

Let us denote the pass in 1^st test, 2^nd test by

Sjands

P(Si) = 0.7 P(S2) = 0.75 P(Sin S2) = 0.65

Given the student failed in first test, the probability that student will pass in second test is given by

P(S2 n (1 - 1) P (S251) = P(1 - S1) 0.1 0.3 = 0,3333

B

Probability of success

P=

Variance of winning is given by

V =n.p: (1 – p) =10.. (1- = 0.24375

For n=100 the standard deviation is

S.D = Vn.p: (1-P) - 100.0 (1) = 1.561