Steve has 8 biscuits in a tin. There are 5 digestive and 3 chocolate biscuits. Steve takes two biscuits at random from the tin. Work out the probability that he chooses two different types of biscuits.

Probability that he chooses two different types of biscuits is 53.65 %.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it.

Given

Total biscuits, n = 8

Digestive biscuits = 5

Chocolate biscuits = 3

There are two patterns to chose two different biscuits; a digestive then a chocolate or a chocolate and then a digestive.

∴ The probability of choosing a digestive then a chocolate

= [tex]\frac{5}{8}\times\frac{3}{7}[/tex]

= [tex]\frac{15}{56}[/tex]

= 0.267

The probability of choosing chocolate and then a digestive.

= [tex]\frac{3}{8} \times\frac{5}{7}[/tex]

= [tex]\frac{15}{56}[/tex]

= 0.267

Hence, The combined probability

= [tex]\frac{15}{56}+ \frac{15}{56}[/tex]

= [tex]0.536[/tex]

= 53.6 5 %

Probability that he chooses two different types of biscuits is 53.65 %.

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