Question

5.

A dice is biased so that it lands on 1 one quarter of the time. It lands on 3 twice as often as it land on 2 and
three times as often as it lands on 4. It lands on 5 ten percent more often than it lands on 4 and ten percent
less often than it lands on 6. If I roll the dice 350 times, how often should I expect to roll a 6?

Answer 1

91

Explanation:

P(1) = 0.25

P(3) = 2P(2) = 3P(4)

P(5) = P(4) + 0.1 = P(6) − 0.1

The probabilities add up to 1:

1 = P(1) + P(2) + P(3) + P(4) + P(5) + P(6)

Write each probability in terms of P(4).

1 = 0.25 + 1.5P(4) + 3P(4) + P(4) + P(4) + 0.1 + P(4) + 0.2

1 = 0.55 + 7.5P(4)

0.45 = 7.5P(4)

P(4) = 0.06

Therefore, P(6) = P(4) + 0.2 = 0.26.

The expected value is the number of trials times the probability.

E = 350 × 0.26

E = 91