Find the mean number of heads in three tosses of a fair coin.
Answers
Answer:
the mean number of heads in three tosses of a fair coin = 1.5
Step-by-step explanation:
three tosses of a fair coin.
have 2 * 2 * 2 = 8 Ways
HHH , HHT , HTH , HTT , THH , THT , TTH , TTT
H(0) = 1 (TTT)
H(1) = 3 (HTT , THT , TTH)
H(2) = 3 ( HHT , HTH , THH)
H(3) = 1 (HHH)
Mean = (0 *1 + 1*3 + 2 *3 + 3 * 1)/8
= (0 + 3 + 6 + 3)/8
= 12/8
= 3/2
= 1.5
the mean number of heads in three tosses of a fair coin = 1.5
The mean number of heads in 3 tosses of the coin is 1.5
Step-by-step explanation:
The mean number of heads in 3 tosses of the coin is computed as:
Let X be the Number of heads
Tossing 3 coins simultaneously
We get 0 Heads, 1 Heads, 2 heads or 3 Heads
So, value of X could be 0, 1,2 or 3
X Outcomes Number of Outcomes P(X)
0 (TTT) 1 1/8
1 (THT) , (HTT), 3 3/8
(TTH)
2 (HHT) , (HTT), 3 3/8
(THH)
3 (HHH) 1 1/8
Therefore, the probability distribution is:
X P(X)
0 1/8
1 3/8
2 3/8
3 1/8
Then the mean number is given by:
Mean = X × P(X) + X × P(X) + X × P(X) + X × P(X)
Mean = 0 × 1/8 + 1 × 3/8 + 2 × 3/8 + 3 × 1/8
Mean = 0 + 3/8 + 6/8 + 3/8
Mean = (0 + 3 + 6 + 3) / 8
Mean = 12/ 8
Mean = 1.5