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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.

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Solution

## 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 =$\frac{\mathrm{frequency}\mathrm{of}\mathrm{getting}\mathrm{no}\mathrm{head}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{trails}}=\frac{120}{500}=\frac{6}{25}$

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