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If 10 coins are tossed 100 times, how many times would you expect 7 coins to fall head upward.
  • a)
    14
  • b)
    12
  • c)
    13
  • d)
    11
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If 10 coins are tossed 100 times, how many times would you expect 7 co...
12 is the answer
Step-by-step explanation:
This is the binomial distribution (p+q)^10 with p =1/2, q = 1/2.
You can have 10 heads, probability of this is p^10 or 1/1024
9 heads 1 tail has pr = 10.p.q^9 = 10/1024
8 heads 2 tails has pr = 10C2.p^2.q^8 = 45/1024
7 heads 3 tails has pr = 10C3.p^7.q^3 = 120/1024
So in 100 trials of this you would expect 7 heads & 3 tails to occur 100 x 120/1024 times
or about 11.7 times. Nearly 12 times.
The nearest whole number is 12.
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Most Upvoted Answer
If 10 coins are tossed 100 times, how many times would you expect 7 co...
Expected Value Calculation:

To calculate the expected value, we use the formula:

E(X) = n * p

Where,
n = number of trials
p = probability of success

Here, n = 100 (number of times the coins are tossed)
p = probability of getting heads = 1/2 (since there are two possible outcomes - heads or tails)

So, E(X) = 100 * 1/2 = 50

Now, we need to find the expected number of times 7 coins fall head upward. This is a binomial distribution problem, and we can use the formula:

P(X = k) = nCk * p^k * (1-p)^(n-k)

Where,
n = number of trials
p = probability of success
k = number of successes

Here, n = 10 (number of coins tossed)
p = probability of getting heads = 1/2
k = 7 (number of coins falling head upward)

So, P(X = 7) = 10C7 * (1/2)^7 * (1/2)^3 = 120 * 1/128 * 1/8 = 15/256

Now, to find the expected number of times 7 coins fall head upward, we multiply the probability by the number of trials:

E(X) = n * P(X = k)

E(7 heads out of 10 tosses) = 100 * (15/256) = 1.171875

Rounding this value to the nearest integer, we get 12.

Therefore, the correct answer is option B, 12.
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If 10 coins are tossed 100 times, how many times would you expect 7 coins to fall head upward.a)14b)12c)13d)11Correct answer is option 'B'. Can you explain this answer?
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