Question

Two coins are tossed simultaneously 500 times and the outcomes are noted as given below:

Outcome:	Two heads (HH)	One head (HT or TH)	No head (TT)
Frequency:	105	275	120

If same pair of coins is tossed at random, find the probability of getting (i) Two heads (ii) One head (iii) No head.

Answer 1

Number of trials = 500
Number of outcomes of two heads (HH) = 105
Number of outcomes of one head (HT or TH) = 275
Number of outcomes of no head (TT) = 120

(i) Probability of getting two heads =$\frac{\mathrm{frequency}\mathrm{of}\mathrm{getting}2\mathrm{heads}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{trails}}=\frac{105}{500}=\frac{21}{100}$

(ii) Probability of getting one head =$\frac{\mathrm{frequency}\mathrm{of}\mathrm{getting}1\mathrm{head}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{trails}}=\frac{255}{500}=\frac{11}{20}$

(iii) Probability of getting no head =$\frac{\mathrm{frequency}\mathrm{of}\mathrm{getting}\mathrm{no}\mathrm{head}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{trails}}=\frac{120}{500}=\frac{6}{25}$