Question

There are four pens: Red, Green, Blue, and Purple in a desk drawer of which two pens are selected at random one after the other with replacement. State the sample space and the following events. 

(a) A : Select at least one red pen. 

(b) B : Two pens of the same colour are not selected.

Answer 1

The drawer contains 4 pens out of which one is red (R), one is green (G), one is blue (B) and the other one is purple (P). 

From this drawer, two pens are selected one after the other with replacement. 

∴ The sample space S is given by S = {RR, RG, RB, RP, GR, GG, GB, GP, BR, BG, BB, BP, PR, PG, PB, PP} 

(a) A : Select at least one red pen. At least one means one or more than one. 

∴ A = {RR, RG, RB, RP, GR, BR, PR}

(b) B : Two pens of the same colour are not selected. 

B = {RG, RB, RP, GR, GB, GP, BR, BG, BP, PR, PG, PB}