Bella flips a coin

Probability is $\dfrac{\text{\# of favorable outcomes}}{\text{\# of possible outcomes}}$ . We don't have to worry about anything else because heads and tails are equally likely in this case. The number of favorable outcomes is the number of ways to choose $7$ of the $10$ spots to be heads. This is simply $\dbinom{10}{7}$ , or $120$ . There are $2$ possible outcomes for each flip, so the number of possible outcomes is $2^{10}$ , or $1024$ . Thus the answer is $\dfrac{120}{1024} = \dfrac{15}{128}$

1st coin toss can give 2 result (H or T). Similarly in other toss this can happen. $$ So, total possible outcome = 2x2x2x.......2 = 2¹⁰ $$ And total favorable outcome = ¹⁰C₇ $$ Hence Probability, P = ¹⁰C₇ / 2¹⁰ = 15/128

This is a direct consequence of Bernoulli Distribution which says that, /[ f(k)=\frac{m!}{k!(m-k)!}Power(p)^{k}Power(1-p)^{N-k}; where k is total number of required outcome and N is total no of possible outcomes, also p=probability of favorable outcome. Putting N=10, k=7 and p=1/2 we'll get required probability.

P( of getting heads 7 times out of 10 times tossed) = 10!/{7! (10-7)!)} (1/2)^7*(1/2)^3

According to the formula of BIONOMIAL DISTRIBUTION, P(x)=nCx p^x q^(n-x) P(x)=10C7 (1/2)^7 (1/2)^3 P(x)=15/128 THE ANSWER IS 15/128.

The probability of exactly 5 heads is 1/2. The probability of 7 heads has to be less than 1/2. Of the choices, only one was less than 1/2. 15/128 has to be the answer.

Probability will be expected results/possible results. to get 7 heads out of 10 and possible results 2 raise to power 10. so,we get 120/1024 =15/128 Ans.

K.K.GARG.India

Nice. Devide it by 120/2048

this is a simple question of binomial distribution

I eliminated 1/2, 2, 3/5 as being too simple when a number like 7 is involved, so I got the right answer without worrying about probablility.

WAS MY APPROCH CORRECT PLZ TELL

ACTULLY I FORGOT THZ COMBNATION THING ... THN ALSO IT WAS EASY FOR ME BECZ UR FIRST OBTION WAS 2 WHICH IS NOT POSSIBLE PROBABILITY CAN NOT B MORE THEN 1 AND 3RD OBTION WAS MORE THN .5 WHICH IS AGAIN NOT POSSIBLE BECZ LESS THEN 5 TAILS PROBABILITY WAS ASKED.. AND FORTH OBTION WAS .5 WHICH IS ALSO NOT POSSIBLE BECASE IT HAS LESS THEN HALF OF TAILS..

This is how i solved it :

C(10,7)/2^10 = 15/128

it is just a simple binomial question , X~B(10,0.5)