Question

A roulette wheel has 38 slots, 18 are red, 18 are black, and 2 are green.You play five games and always bet on red. a) How many games can you expect to win? b) What is the probability that you will win all five games? c) If you win three or more games, you make a profit. If you win two or fewer games, you lose money. What is the probability that you will win no more than two games?

Answer 1

Answer:

a) 2.35 games.

b) Therefore, the probability is P=0.0229.

c) Therefore, the probability is P=0.71.

Step-by-step explanation:

We know that a roulette wheel has 38 slots, 18 are red, 18 are black, and 2 are green.You play five games and always bet on red.

Therefore, we have

$p=\frac{18}{38}=0.47\\\\q=\frac{20}{38}=0.53$

a) We  can you expect to win 5·0.47= 2.35 games.

b) We calculate the  probability that you will win all five games.

$P=C_5^5\cdot p^5\cdot q^0\\\\P=1\cdot 0.47^5 \cdot 0.53^0\\\\P=0.0229$

Therefore, the probability is P=0.0229.

c)  We calculate the probability that you will win  three or more games.

$P=1-C_2^5\cdot 0.47^3\cdot 0.53^2\\\\P=1-10\cdot 0.47^3\cdot 0.53^2\\\\P=1-0.29\\\\P=0.71$

Therefore, the probability is P=0.71.