# Sample Spaces and Events

Printable View

• April 3rd 2009, 12:13 AM
youvy
Sample Spaces and Events
43. From a group of 20 men and 16 women, 2 people are chosen at random. Find the probability of:

a) 1 man and 1 woman being chosen
b) 2 men being chosen
c) 2 women being chosen

Thank you:)
• April 3rd 2009, 12:35 AM
toop
a. 1 man being chosen = 20/36 and 1 woman being chosen is 16/36

The probability of both would be the product of the two probabilities I believe.

b. The probability of the first man being chosen is 20/36 and the probability of the second is 19/35 since you are now one man down. Multiply the two probabilities.

c. The probability of the first woman being chosen is 16/36 and the second is 15/35. Multiply the two like above.
• April 3rd 2009, 03:19 AM
mr fantastic
Quote:

Originally Posted by toop
a. 1 man being chosen = 20/36 and 1 woman being chosen is 16/36

The probability of both would be the product of the two probabilities I believe.

b. The probability of the first man being chosen is 20/36 and the probability of the second is 19/35 since you are now one man down. Multiply the two probabilities.

c. The probability of the first woman being chosen is 16/36 and the second is 15/35. Multiply the two like above.

I don't think your solution to (a) is correct.

The correct answer is given by $\frac{{20 \choose 1} \cdot {16 \choose 1}}{{36 \choose 2}} = \frac{20 \cdot 16 \cdot 2}{36 \cdot 35} \, ....$
All times are GMT -8. The time now is 06:57 AM.
Copyright © 2005-2013 Math Help Forum. All rights reserved.
Copyright © 2005-2013 Math Help Forum. All rights reserved.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.949122965335846, "perplexity_flag": "middle"}