If a fair coin is tossed 10 times, find the probability of (i)         exactly six heads        (ii)        at least six heads (iii)       at most six heads

Explanation

`a)` Probability of exactly six heads `= \ ^10 C_6 (0.5)^10`


`b)` Probability of at least `6` heads `= \ ^10 C_6 (0.5)^10 + \ ^10 C_7 (0.5)^10 + \ ^10 C_7 (0.5)^10 + 8\ ^10 C_9 (0.5)^10 + \ ^10 C_10 (0.5)^10`

`=386/1024`



`c)` Probability of at most `6` heads `= 1 - \ ^10 C_7 (0.5)^10 + \ ^10 C_8 (0.5)^10 +\ ^10 C_9 (0.5)^10 +\ ^10 C_10 (0.5)^10`

`=848/1024`