A biased dice is thrown.
The probability of the dice landing on 1,2,3,4 and 5 are shown:
1 = 0.14
2 = 0.07
3 = 0.21
4 = 0.15
5 = 0.16
6 = ?
The dice is thrown 200 times.
How many times should we expect the dice to land on either a 2 or a 6?
To find the probability of the dice landing on either a 2 or a 6, we add the probabilities of landing on 2 and landing on 6:
P(2 or 6) = P(2) + P(6)
We are given the probability of landing on a 2, which is 0.07, but we need to find the probability of landing on a 6. Since the probabilities for all the other numbers are given, and the sum of all probabilities must be 1, we can subtract the sum of the probabilities for 1, 2, 3, 4, and 5 from 1 to find the probability of landing on a 6:
P(6) = 1 - (P(1) + P(2) + P(3) + P(4) + P(5))
P(6) = 1 - (0.14 + 0.07 + 0.21 + 0.15 + 0.16)
P(6) = 1 - 0.73
P(6) = 0.27
Now we can calculate the expected number of times the dice should land on either a 2 or a 6 out of 200 throws:
Expected number = Total throws × Probability of landing on 2 or 6
Expected number = 200 × (P(2) + P(6))
Expected number = 200 × (0.07 + 0.27)
Expected number = 200 × 0.34
Expected number = 68
Therefore, we should expect the dice to land on either a 2 or a 6 approximately 68 times out of 200 throws.