Probability Q help THX

[BlueShrimp93]

If 10 coins are tossed 50 times, in how many cases would we expect the number of heads to exceed the number of tails? (Ans: 19)

Much appreciated,

[fun_jirachi]

Hi there

Note that there are three possible outcomes when tossing the 10 coins:
No. of heads = No. of tails (ie. 5 heads, 5 tails)
No. of heads < No. of tails (ie. 0, 10; 1, 9; 2, 8; 3, 7; 4, 6)
No. of heads > No. of tails (ie. 10, 0; 9, 1; 8, 2; 7, 3; 6, 4)

Because the probability of tossing a tail is equal to the probability of tossing a head, we can cheat a little bit by noticing that the probability of more tails than heads is the same as the probability of tossing more heads than tails.

Basically, we note that


Hope this helps

[BlueShrimp93]

Awesome thanks so much