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To demonstrate probabilities, a mathematics teacher had students draw cards from a bag which contained 26 red cards and26 black cards. During class, the bag was dropped, and 4 red cards and 2 black cards were lost.Tell whether the loss of cards changes the probability of drawing a black card from the bag.If so, was the probability increased or decreased? Support your answer by calculating the probability for each situation.

Respuesta :

The probability of an event is given by the following formula:

[tex]P(X)=\frac{Number\text{ of favorable outcomes to X}}{\text{Total number of possible outcomes}}[/tex]

The total number of possible outcomes is the total number of red and black cards in the bag.

The favorable outcomes to drawing a black card in the first situation are 26 (because there are 26 black cards).

The probability of drawing a black card before the bag was dropped was:

[tex]P(\text{black card)=}\frac{26}{26+26}=\frac{26}{52}=0.5[/tex]

After the bag was dropped, the total number of cards is:

Red cards= 26-4=22 and Black cards=26-2=24 cards.

Total number of cards=22+24=46.

The probability of drawing a black card after the bag was dropped is:

[tex]P(\text{black card)=}\frac{24}{46}=0.52[/tex]

Thus, the probability of drawing a black card from the bag increased.

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